There has been a large body of work on trees determined by their combinatorial Laplacian spectra, partly due to the interest generated by the survey paper of van Dam and Haemers [1]}, which asked more generally, which graphs are determined by their spectra for various matrices associated with a graph. In their concluding remarks [1]}, they noted that resolving the question for general graphs seemed out of reach, and proposed the more tractable problem of classifying which trees are determined by their spectra.
